Completly beveling edges on model
If you do triangulate (ctrl+T) you can see why you have problems with your mesh structure (you have some Poylgon-faces there which will be exposed by this)

I would strongly suggest to do some manual retopology to clean the mesh base structure. It is really not that hard as it sounds. 

The easiest way to do this would be to just select some points, copy and seperate them from that object and than connect them to make nice quad-faces, then you could use edge slide (press "g" twice) to make the positioning of the vertices more even if you need to... etc.:



So you can see how the geometry affects the subdivusion surface behavior here is a comparison: (your faces above, quick manual retopology below) 



If you want to maximally reduce the real geometry you can apply the modifier, select the loop cut with Alt-select and delete it with "dissolve edges":